Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp

In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem....

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Autores principales: Acosta Rodriguez, Gabriel, Armentano, Maria Gabriela, Duran, Ricardo Guillermo, Lombardi, Ariel L.
Publicado: 2005
Materias:
Cuspidal domains
Neumann problem
Regularity
Traces
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v310_n2_p397_Acosta
http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0022247X_v310_n2_p397_Acosta2023-06-08T14:47:50Z Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp Acosta Rodriguez, Gabriel Armentano, Maria Gabriela Duran, Ricardo Guillermo Lombardi, Ariel L. Cuspidal domains Neumann problem Regularity Traces In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v310_n2_p397_Acosta http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cuspidal domains
Neumann problem
Regularity
Traces
spellingShingle Cuspidal domains
Neumann problem
Regularity
Traces
Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
Duran, Ricardo Guillermo
Lombardi, Ariel L.
Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
topic_facet Cuspidal domains
Neumann problem
Regularity
Traces
description In this work we analyze the existence and regularity of the solution of a nonhomogeneous Neumann problem for the Poisson equation in a plane domain Ω with an external cusp. In order to prove that there exists a unique solution in H1 (Ω) using the Lax-Milgram theorem we need to apply a trace theorem. Since Ω is not a Lipschitz domain, the standard trace theorem for H1 (Ω) does not apply, in fact the restriction of H1 (Ω) functions is not necessarily in L2 (∂Ω). So, we introduce a trace theorem by using weighted Sobolev norms in Ω. Under appropriate assumptions we prove that the solution of our problem is in H2 (Ω) and we obtain an a priori estimate for the second derivatives of the solution. © 2005 Elsevier Inc. All rights reserved.
author Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
Duran, Ricardo Guillermo
Lombardi, Ariel L.
author_facet Acosta Rodriguez, Gabriel
Armentano, Maria Gabriela
Duran, Ricardo Guillermo
Lombardi, Ariel L.
author_sort Acosta Rodriguez, Gabriel
title Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
title_short Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
title_full Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
title_fullStr Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
title_full_unstemmed Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp
title_sort nonhomogeneous neumann problem for the poisson equation in domains with an external cusp
publishDate 2005
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v310_n2_p397_Acosta
http://hdl.handle.net/20.500.12110/paper_0022247X_v310_n2_p397_Acosta
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AT duranricardoguillermo nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
AT lombardiariell nonhomogeneousneumannproblemforthepoissonequationindomainswithanexternalcusp
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